Norm forms for arbitrary number fields as products of linear polynomials

@article{Browning2013NormFF,
  title={Norm forms for arbitrary number fields as products of linear polynomials},
  author={T. Browning and Lilian Matthiesen},
  journal={arXiv: Number Theory},
  year={2013}
}
Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. We show that any smooth model of the affine variety defined by the equation N_{K/Q} (k) = P(t) satisfies the Hasse principle and weak approximation whenever the Brauer-Manin obstruction is empty. Our proof is based on a combination of methods from additive combinatorics due to Green-Tao and Green-Tao-Ziegler, together with an application of the descent theory of Colliot-Th… Expand
Strong approximation and descent
Strong approximation for a family of norm varieties
On the fibration method for zero-cycles and rational points
Arithmetic and Geometry: A survey of applications of the circle method to rational points
On the equation N_{K/k}(\Xi)=P(t)
Asymptotics for some polynomial patterns in the primes
  • Pierre-Yves Bienvenu
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2019
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